(a) Field of the Invention
The present invention relates to an F-.theta. lens system to be used in a plane scanning optical system.
(b) Description of the Prior Art
There has conventionally been known a plane scanning optical system as shown in FIG. 1. In this optical system, the reference numeral 1 represents a light source. The light beam 2 emitted from this light source is reflected by a rotating polygonal mirror 3 and then focused by an imaging lens 4 as a spot 6 on a scanned surface 5. When the polygonal mirror 3 is rotated in the direction indicated by the arrow A, the spot 6 travels on the scanned surface 5 in the direction indicated by the arrow B. Since it is necessary to travel the spot 6 at a constant speed on the scanned surface 6, it is impossible to use an ordinary photographic lens as the imaging lens 4.
In case of an ordinary photographic lens in which distortion is corrected favorably, there establishes the following relationship among field angle .theta., focal length f and image height y: EQU y=f.multidot.tan .theta. (1).
As is clear from the formula (1) above, the image height y varies in proportion to tangent of the field angle .theta.. Therefore, when such a lens system as an ordinary photographic lens system having favorably corrected distortion is used as the imaging lens 4, rotation of the polygonal mirror at a constant speed causes variation of .theta. at a constant rate and faster travelling of the spot 6 at peripherical portion of the scanned surface 5, thereby making it impossible to scan at a constant speed.
As a method to eliminate the above-said defect or travel the spot at a constant speed on the scanned surface, thereby is contrived a method to control the rotating speed of the polygonal mirror so as to travel the spot at a constant speed without rotating said mirror at a constant speed. However, this method is actually accompanied by numerous difficulties and not practical though it is theoretically possible.
As another method to travel the spot at a constant speed on the scanned surface, there has been contrived a method to use the so-called f-.theta. lens system as the imaging lens. It is a lens system meeting the relationship among image height y, focal length f and field angle .theta. expressed by the following formula (2): EQU Y=f.multidot..theta. (2).
When actual image height is designated by y', distortion D is generally expressed by the following formula (3): ##EQU1##
In contrast, distortion in the f-.theta. lens system is expressed by the following formula (4): ##EQU2##
Hence, in the f-.theta. lens system in which distortion D' expressed by the formula (4) is corrected to zero, the ordinary distortion D has a large negative value.
The F-.theta. lens system must have the other aberrations so corrected as to obtain a spot shape close to diffraction limit in addition to the distortion D' so corrected as to assure constant-speed travelling of the spot described above.
Spot diameter d is expressed by the following formula (5): EQU d=k.multidot.F.multidot..lambda. (5)
wherein the reference symbol F represents F number of the imaging lens, the reference symbol .lambda. designates wavelength of the light beam used and the reference symbol k denotes a constant.
Since the reference symbols k and .lambda. have predetermined values respectively in the above formula (5), it is necessary to minimize value of F for the purpose of obtaining a small diameter d.
On the other hand, plane scanning optical systems using such an f-.theta. lens system are utilized in various fields in the recent days. These fields demand small plane scanning optical systems. For meeting this demand, it is necessary to design a wide-angle f-.theta. lens system. In addition, it is necessary to minimize F number for the purpose of enhancing resolution. Furthermore, it is required to compose the lens system of a small number of lens elements for the purpose of manufacturing it at a low cost.
As the conventional f-.theta. lens systems, there have already been known the ones disclosed by Japanese unexamined published patent application Nos. 53308/80 and 150144/79. However, the lens system disclosed by the former has a drawback that it is composed of a large number of lens elements and highly priced. The lens system disclosed by the latter has a narrow field angle and a large F number though it is composed of a small number of (three or four) lens elements.